5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is?<p></p>

Given¯x=∑xi5=150⇒5∑i=1xi=750(i)σ2=18∑x2i5−(¯x)2=18∑x2i5−(150)2=18∑x2i=112590 (ii)Given height of new student x6=156Now,¯xnew=5∑i=1xi6=750+1566=151Also,σ2new=5∑i=1x2i6−(¯xnew)2=112590+(156)26−(151)2=22821−2801=20.

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Question:

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is?

Solution: